Answer:
there are 8 candles
Step-by-step explanation:
(i) In order to obtain an equal amount of candle to candle holders Caroline has to buy enough packs to obtain a 1:1 ratio.
Therefore to obtain a 1:1 ratio:
=30 candles/18 candle holders * (18/30)
Therefore she needs to buy 18 packs of candles and 30 packs of candle holders to have exactly the same number of candles and holders
(ii) Caroline can make = 30*18 = 540 table decorations
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The answer is A
Hope this helps!!
P = perimeter
L = length
W = width
Formula for the perimeter of a rectangle = L + L + W + W or P = 2L + 2W
You know:
P = 110ft
L = W + 5 [length is 5ft greater than the width]
So plug this into the formula:
P = 2L + 2W Substitute/plug in (W + 5) for L
110 = 2(W + 5) + 2W Distribute/multiply 2 into (W + 5)
110 = (2)W + (2)5 + 2W
110 = 2W + 10 + 2W Combine like terms (2W + 2W)
110 = 4W + 10 Subtract 10 on both sides
110 - 10 = 4W + 10 - 10
100 = 4W Divide 4 on both sides to get "W" by itself
25 = W Now that you know the width, plug it into the equation for length
L = W + 5 Plug in 25 for W
L = 25 + 5
L = 30
L = 30 ft
W = 25 ft
PROOF
P = 2L + 2W
110 = 2(30) + 2(25)
110 = 60 + 50
110 = 110
***Not sure which one you want to be solved but some of the ones with answers are wrong, so I will be explaining those as well with answers; the questions will be labeled 1-4 from top to bottom as shown in your picture***
#1.
Answer:
y=3x+4
Explanation:
The slope is 3 because every 1 unit to the right, the next point is increased by 3. In other words, the line rises 3 every 1 across. Slope is calculated by rise divided by run, in this graph the rise is 3 and the run is 1.
Slope= rise/run=3/1=3
The slope is not negative because it rises upwards from left to right; not downwards as a negative slope would.
Slope-intercept form is y=mx+b with m being slope, b being the y-intercept, and (x,y) being the set of points. The y-intercept is found as the point that intersects on the y axis, here being 4. So, the answer is y=3x+4.
#2.
Answer:
y=(1/2)x+3
Explanation:
Again, y-intercept form is y=mx+b. Here we are given the slope and the x-intercept(the y is 0). Because the slope is given, we can plug that in the slope-intercept equation right away:
y=(1/2)x+b
Now, we just need to find b. So, how can we solve for b? We need to make b the only variable in this equation. This can be done by plugging in the given point, (-6, 0). Here is how b is solved:
y=(1/2)x+b
0=(1/2)(-6)+b
0=-3+b
3=b
So, the equation is y=(1/2)x+3.
#3.
Answer:
y=3x+7
Explanation:
Two points are given. Slope can be found given two points and we can use the slope to create an equation in point-slope form, before solving for the slope-intercept form. Slope can be found using the equation:
m=(y2-y1)/(x2-x1)
This equation basically finds the rise and run of the slope before dividing to find the slope. Plugging in the points given for this problem and find slope is shown below: ((-2, 1) and (1, 10) are the points btw)
m=(10-1)/(1+2)
m=9/3
m=3
Now that we know the slope, we can pick one number to create point-slope form and then move the variables around to create slope-intercept form.
Point-slope form: (y-y1)=m(x-x1)
With variables: (y-1)=3(x+2)
Now, we can use this equation to create slope-intercept form:
(y-1)=3(x+2)
y-1=3x+6
y=3x+7 <—Final Answer!
#4.
Answer:
(y+2)=1/6(x-9)
Explanation:
Given the point and a slope, we can create the point-slope equation. (9,-2) and m=1/6 is given. Refer back to point slope form (y-y1)=m(x-x1). m is the slope and (x1, y1) is the point plugged in.
So, when you plug in the slope and the points you get (y+2)=1/6(x-9).
